Conservation Properties of Unstructured Finite-Volume Mesh Schemes for the Navier-Stokes Equations

Abstract

The Navier-Stokes equations describe fluid flow by conserving mass and momentum. There are two main mesh discretizations for the computation of these equations, the collocated and staggered schemes. Collocated schemes locate the velocity field at the same grid points as the pressure one, while staggered discretizations locate variables at different points within the mesh. One of the most important characteristic of the discretization schemes, aside from accuracy, is their capacity to discretely conserve kinetic energy, specially when solving turbulent flow. Hence, this work analyzes the accuracy and conservation properties of two particular collocated and staggered schemes by solving various problems.

Acknowledgments

This work has been financially supported by the Ministerio de Economía y Competitividad, Secretaría de Estado de Investigación, Desarrollo e Innovación, Spain (ENE-2010-17801), a FPU grant by the Ministerio de Educación, Cultura y Deporte, Spain (AP-2008-03843), and by Termo Fluids S.L.

The authors would like to acknowledge sincerely Ivette Rodríguez, Ricard Borrell, and Carlos David Pérez-Segarra for providing their numerical data of the turbulent flow over a circular cylinder at Re = 3,900.